The previous post in this series discussed the lay of the (is)land from the perspective of TSL (I’m so disappointed in myself for not making this pun last time; better late than never). I mentioned that the TSL view cannot handle all island constraints. Sometimes, we need an alternative approach. But this alternative approach doesn’t come out of nowhere. It is also what we need for all kinds of licensing constraints, and it also handles restrictions on movement that are not island constraints.

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In the previous post we saw Merge is SL-2 over dependency trees, and Move is TSL-2. For every movement feature f we project a separate tier that contains only lexical items that have a licensor feature f⁺ or a licensee feature f^-. A tier is well-formed iff every lexical item with a licensee feature has a mother with a licensor feature, and every lexical item with a licensor feature has exactly one lexical item among its daughters that carries a licensee feature. It’s a pretty simple system. Despite that simplicity, it predicts a fundamental aspect of movement: island effects!

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Alright, syntax. Things are gonna get a bit more… convoluted? Nah, interesting! In principle we’ll see a lot of the same things as in phonology, and that’s kind of the point: phonology and syntax are actually very similar. But syntax isn’t quite as exhibitionist as phonology, it doesn’t show off its subregular complexity in the open for the world to see. So the first thing we’ll need is a suitable representation. Once we have that, it’s pretty much phonology all over again, but now with trees.

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After a brief interlude, let’s get back to locality. This post will largely act as a recap of what has come before and provide a segue from phonology to syntax. That’s also a good time to look at the bigger picture, which goes beyond putting various phenomena in various locality boxes just because we can.

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Pro tip: Don’t start a multi-part series of posts on locality right before the beginning of the semester and when you have a pile of papers to review. On the upside, this will give you guys some extra time to digest all the concepts in the three previous posts. In the meantime, here’s a quick and dirty post on corpus linguists and why it should be part of our syntax curriculum. I didn’t even proofread it, so beware.

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We’re continuing our stroll through the subregular locality zoo, still in the service of ultimately being able to say something about syntax and its interface with PF and LF. We started out with SL as the most restrictive kind of locality. The step to the TSL region corresponds to a relativized notion of locality where it’s not absolute locality that matters, but your position relative to other elements of a specific type. TSL is actually a cluster of different classes, with standard TSL at the very bottom. Depending on what context information the TSL tier projection may take into account, TSL expands to ITSL, OTSL, or IOTSL. While IOTSL has a very liberal notion of locality that can even accommodate insane patterns like nati, it still involves some level of locality. That’s in stark contrast to the strictly piecewise (SP) dependencies of Rogers, Heinz, Bailey, Edlefsen, Vischer, Wellcome, and Wibel (2010), which throw locality out the window.

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The previous post covered the essentials of strictly local (SL) and tier-based strictly local (TSL) dependencies over strings. We saw that even though TSL generalizes SL to a relativized notion of locality, it is still a restrictive model in the sense that not every non-local dependency is TSL. In principle that’s a nice thing, but among those non-local dependencies beyond the purview of TSL we also find some robustly attested phenomena like unbounded tone plateauing. Fair enough, but that does not mean that unbounded tone plateauing is entirely non-local.

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Omer has a recent post on listedness. I have a post coming up that expands on my comments there, but it isn’t really fit for consumption without prior knowledge of subregular complexity and how it intersects with the linguistic concept of locality. So I figured I’d first lead in with a series of posts as a primer on some of the core concepts from subregular complexity. I’ll start with phonology — for historical reasons, and because the ideas are much easier to grok there (sorry phonologists, but it’s a playground compared to syntax). That will be followed by some posts on how subregular complexity carries over from phonology to syntax, and then we’ll finally be in a position to expand on Omer’s post. Getting through all of this will take quite a while, but I think it provides an interesting perspective on locality. In particular, we’ll see that the common idea of “strict locality < relativized locality < non-local” is too simplistic.

With all that said, let’s put on our computational hats and get going, starting with phonology. Or to be more specific: phonotactics.

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I promised, and you shall receive: a KISS account of a particular aspect of semantics. Remember, KISS means that the account covers a very narrowly circumscribed phenomenon, makes no attempt to integrate with other theories, and instead aims for being maximal simple and self-contained. And now for the actual problem:

It has been noted before that not every logically conceivable quantifier can be realized by a single “word”. Those are very deliberate scare quotes around word as that isn’t quite the right notion — if it can even be defined. But let’s ignore that for now and focus just on the basic facts. We have every for the universal quantifier \(\forall\), some for the existential quantifier \(\exists\), and no, which corresponds to \(\neg \exists\). English is not an outlier, these three quantifiers are very common across languages. But there seems to be no language with a single word for not all, i.e. \(\neg \forall\). Now why the heck is that? If language is fine with stuffing \(\neg \exists\) into a single word, why not \(\neg \forall\)? Would you be shocked if I told you the answer is monotonicity? Actually, the full answer is monotonicity + subregularity, but one thing at a time.

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I just got back from MOL (Mathematics of Language) in Toronto, and much to my own surprise I actually got to talk some more about KISS theories there. As you might recall, my last post tried to made a case for more simple accounts that try to handle only one phenomenon but do so exceedingly well without the burden of machinery that is needed for other phenomena. My post only listed two examples for syntax as I was under the impression that this is a rare approach in linguistics, so I didn’t dig much deeper for examples. But at MOL I saw Yoad Winter give a beautiful KISS account of presupposition projection (here’s the paper version). That’s when it hit me: in semantics, KISS is pretty much the norm!

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